Since you have a number of numerical exercises in the book, I will concentrate here on conceptual and applied problems.
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1) An isothermal reaction, A--> B, is endothermic and yet spontaneous. What is the sign of the entropy change in the system? What is the sign of the entropy change in the environment (everything outside the system)? Which one has the largest magnitude (absolute value) the entropy change outside the system or the entropy change inside the system?
2) In certain preparative procedures in biochemical labs it is necessary to make up solutions with very high CsCl concentrations. Upon adding the CsCl to water, one finds that the beaker becomes extremely cold. Explain this in terms of entropy and enthalpy changes associated with dissolving this salt.
3) A spontaneous reaction occurs inside an adiabatic system. Is the entropy change in the environment around the system positive negative or zero? Is the entropy change inside the system positive, negative or zero?
4) The following is a problem presented to me by one of you and I thought it was instructive. What is the entropy change associated with the adiabatic, reversible expansion of an ideal gas?
5) Use the Clausius inequality (dS >= dq/T) to argue that the most work you can get from a system is when the work is done reversibly.
6) It is said that for any spontaneous process in the Universe, the overall entropy change will be positive. This is the second law of thermodynamics. Given this, explain how something as ordered as life could have spontaneously arisen on the earth. (For those of you whose religious beliefs tell you that life did not arise spontaneously, just explain why it is thermodynamically possible for life to have arisen spontaneously -- this does not, of course, prove that it did.)
7) For a system at constant temperature and pressure, explain why (in terms of entropy changes in the system and its environment) at equilibrium the enthalpy change (deltaH) and the temperature times the entropy change (T x deltaS) are equal.
8) For a solid/liquid transition, explain in terms of the specific temperature dependence of the chemical potential why liquid is favored over solids as the temperature is increased.
9) For a liquid/gas transition, explain in terms of the specific temperature dependence of the chemical potential why gas is favored over liquid as the temperature is increased.
10) For a solid/liquid transition, explain in terms of the specific pressure dependence of the chemical potential why liquid is favored over solids as the pressure is decreased.
11) For a liquid/gas transition, explain in terms of the specific pressure dependence of the chemical potential why gas is favored over liquid as the temperature is decreased.
12) Why, in terms of entropy, is the flow of heat from a hot source to a cold source spontaneous. Your answer should specifically consider the entropy changes associated with the heat transfer in the two sources separately.
13) Internal combustion engines, such as the one in a car, involve an essentially adiabatic expansion upon rapid internal heating from the reaction of gasoline with oxygen (this is the up stroke of the piston). On the down stroke of the piston, the expanded, hot gas is expelled from the chamber into the exhaust manifold. It turns out that the relative temperature of the engine and the exhaust manifold in part determine the efficiency of this process. For maximum efficiency, which should be hotter, the engine or the exhaust manifold? Why does this have an effect on the engine’s efficiency?
14) What (in words, not equations) is the relationship between the chemical potential and the Gibbs free energy of a pure substance?
15) Describe the standard state of a gas.
16) What is the critical point and what happens to a liquid/gas interface if you heat it above the critical point?
17) What is the triple point and why is it different from other points along the solid/liquid phase boundary?
18) Endothermic reactions that are spontaneous at high temperature are usually not spontaneous at low temperature. Why? (For this problem, assume that the change in entropy for the reaction is temperature independent.)
19) Let’s say you are working for NASA and one of the new engineers working in your group comes up with a new plan to power space ships. “It is simple.” he says “All we need to do is to bring up a canister of compressed air. When we release the air from the confined volume of the canister into the infinite volume of space (which is essentially a vacuum), thermodynamics tells us that the entropy change will be infinite and therefore we will be able to perform an infinite amount of work using that entropy change as a driving force.” What is wrong with this proposal?
20) Consider a glass of ice water with a freely flexible diaphragm covering it (thus the pressure inside is atmospheric pressure, but the system is closed. There is an air space over the ice water in the glass and one allows the system to come to equilibrium (assume that no heat goes into or out of the glass). At this point, one has an equilibrium between three phases: ice, water and vapor. Does that mean we are at the triple point of water? Explain.
21) A piston which maintains constant pressure inside contains only liquid water initially. We then begin to heat the piston. Will there be water vapor present at any temperature below the boiling point? Will there be any liquid present at any temperature above the boiling point? What is it that defines the boiling point of a liquid?
22) Do (21) over again, but this time assume that initially an equal volume of 1 atm dry nitrogen gas was added to the piston with the liquid water at the beginning of the experiment.
23) I have a very old air conditioning system on my roof which is not very efficient. It costs me about 100 dollars per month during the peak summer months to cool my house. Energy around here costs about $0.10/kWh (kilowatt hour). My house warms up at a rate of about 10 F per hour on average if I turn the air conditioning off (this is really determined by the temperature of the walls in the house and they don’t change too much in temperature over a 24 hour period). Let’s assume that to a reasonable approximation, the energy required to cool my house would be about the same if the outside temperature was always about at its average value over 24 hrs (about 100 F in the summer). I keep the internal temperature at about 83 F. My house has an area of about 2000 sq ft and the interior walls are about 8 feet high. How much money would I save per month if I replaced my present air conditioning system with a perfect heat pump? The heat capacity of air is about 29 J/(K mol) and the conversion between degrees F and degrees C is degrees F = (degrees C x 1.8) + 32. One kilowatt hour is 3600 kJ. A cubic foot is 28.4 liters.
24) My laboratory does quite a bit of laser spectroscopy. Unfortunately, the lasers are quite sensitive to the relative humidity of the room. In the late summer, the relative humidity outside reaches about 40% at about 40 C. The air in the room comes in directly from the outside after it is cooled to about 20 C. Almost no water is removed from it by the cooling process (unfortunately). The vapor pressure of water at 40 C is about 0.085 atm and that at 20 C is around 0.025 atm. What is the relative humidity inside my laser lab ( relative humidity is the partial pressure of water vapor in the atmosphere divided by the vapor pressure of water at that temperature) assuming that no water is removed from the air as it is cooled going from the outside to the inside?